Problem 3: A projectile is shot from the surface of Earth by means of a very pow

Question

Problem 3:
A projectile is shot from the surface of Earth by means of a very powerful cannon. If the
projectile reaches a height of 35,000 m above Earth's surface, what was the speed of the
projectile when it left the cannon?

Problem 4:
A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless
surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the
equilibrium position.
(a) What is the amplitude of vibration?
(b) At what location are the kinetic energy and the potential energy equal?

Explanation / Answer

conservation of energy. mv^2/2-GMm/6400e3=-GMm/6435e3 so that v^2=677e3 so v=822(m/s). ----------------------- a) kA^2/2=mv^2/2 so A=v*sqrt(m/k)=0.237(m). b) kx^2/2=mvx^2/2=kA^2/4. so that x^2=A^2/2. so x=A/sqrt(2)=+-0.168(m).

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